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General-purpose integrated circuit Perform addition or integration of signals

Chapter 2 Operational amplifiers. General-purpose integrated circuit Perform addition or integration of signals Op amps are most useful when part of the output signals is returned to the input through a feedback network. (closed-loop condition)

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General-purpose integrated circuit Perform addition or integration of signals

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  1. Chapter 2 Operational amplifiers • General-purpose integrated circuit • Perform addition or integration of signals • Op amps are most useful when part of the output signals is returned to the input through a feedback network. (closed-loop condition) • The characteristics of IC op amp (with resistive feedback network) depends on the circuit configuration and the resistive values, but only weekly on the op amp.

  2. Outline • The ideal operational amplifier • The summing-point constraints • The inverting amplifier • The noninverting amplifier • Integrators and Differentiators • Large-signal operation • DC imperfection • Acitve filter

  3. 2.1 The ideal operational amplifier Figure 2.1 Circuit symbol for the op amp. Figure 2.3 Op-amp symbol showing power supplies. Characteristics of an ideal operational amplifier Input resistanceRi voltage gainAdoL  , Acm=0 Output resistanceRo=0

  4. 2.2 The summing-point constraint • The differential input voltage and the input current are zero • Ideal op-amp analysis • Verify that negative feedback is present. • Using summing point constraint. • Apply standard circuit analysis principles to solve for the quantities of interest. v+ = v- i+ = i-=0 i+c v+ v- i-

  5. 2.3 The inverting amplifier i2 • What is the value of v+? • Applying the summing point constraint, What is the value of v-? • Find expressions for the currents flowing through R1 andR2, i1 and i2,in terms of node voltages. • Applying KCL, find an equation for i1, i2 and i- • Derive the closed loop voltage gain Av=vo/vi i1 Negative feedback? Indicate v+ , v- ,i+ and i-

  6. 2.3 The inverting amplifier • Why is it called inverting amplifier? • Input impedance and output impedance Zin=R1, Zo=0 • The virtual-short-circuit (virtual open-circuit) concept

  7. 2.3 The inverting amplifier Variation 1 Figure 2.6 An inverting amplifier that achieves high gain with a smaller range of resistor values than required for the basic inverter.P52）

  8. 2.3 The inverting amplifier Variation 2 Figure 2.7 Summing amplifier. See Exercise 2.1.P53

  9. 2.3 The inverting amplifier Example Figure 2.9 Circuit of Exercise 2.3, p53

  10. 2.4 The noninverting amplifier Figure 2.11 Noninverting amplifier. P55

  11. 2.4 The noninverting amplifier Figure 2.12 Voltage follower. Figure 2.14 Differential amplifier. See Exercise 2.5. P56, refer to p72 figure2.34

  12. Instrumentation-quality differential amplifier P72

  13. Voltage-current converter P73

  14. Current-voltage converter P74

  15. 2.5 Integrators and Differentiators P76

  16. 2.5 Integrators and Differentiators Exercise: Derive the expression for the output voltage vo.

  17. 2.6 Large-signal operation • Output voltage swing (Vomin, Vomax) The range of allowed output voltages before clipping occurs depends on the type of op amp in use, on the load resistance, and on the values of the power-supply voltages. Figure 2.28 For a real op amp, clipping occurs if the output voltage reaches certain limits. Transfer characteristic

  18. 2.6 Large-signal operation • Output current limit (Iomax, mA) • The maximum current that an op amp can supply to a load. • Slew-rate limitation (105~8V/s) • The magnitude of the rate of change of the output is limited. • Full-power bandwidth~(SR,Vomax) • The range of frequencies for which the op amp can produce an undistorted sinusoidal output with peak amplitude equal to the guaranteed maximum output voltage.

  19. 2.7 DC imperfections • bias current IB The average of the DC currents • Offset current Ioff The difference between the bias currents • Offset voltage Voff The output voltage may not be zero for zero input voltage. The op amp behaves as if a small DC source is in series with one of the input terminal.

  20. 2.7 DC imperfections • Cancellation of the effects of bias currents

  21. Pictures of Op Amps

  22. 2.8 Active Filter • Frequency response (P30) • The complex gain: The ratio of the phasor for the output signal to the input signal • Bode plot (P271) • How circuit functions can be quickly and easily plotted against frequency? (straight line approximation & smart scale)

  23. 2.8 Active Filter Logarithmic Frequency Scale A decade is a range of frequencies for which the ratio of the highest frequency to the lowest is 10. An octave is a two-to-one change in frequency.

  24. R1 R2 - + R ~ VO ~ Vs ~ C A filter circuit is designed using an operational amplifier and is shown in the following figure Example (1) Determine the ratio as a function of R,C,R1,R2. (2) Identify whether the circuit is a low-pass, high-pass or band-pass filter, and give reasons. (3) If RC=0.1 and R1/R2=3, sketch the bode plot and find the cut-off frequency.

  25. Summary • Characteristics of an ideal op amp. • The summing-point constraint applies when ideal op amps are used in circuits with negative feedback. • The steps to analyze an ideal op amp circuits. • The inverting/noninverting amplifier • The summing/differentiating amplifier • The integrator/differentiator • The design of simple op amp circuits • Exercise • 2.1, 2.3, 2.5, 2.6, 2.7, 2.9, 2.10, 2.18, 2.19, 2.20, 2.21, 2.22, 2.23(optional)

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